Geometry & Topology, Vol. 9 (2005) Paper no. 26, pages 1147--1185.

Geometry of pseudocharacters

Jason Fox Manning

Abstract. If G is a group, a pseudocharacter f: G-->R is a function which is "almost" a homomorphism. If G admits a nontrivial pseudocharacter f, we define the space of ends of G relative to f and show that if the space of ends is complicated enough, then G contains a nonabelian free group. We also construct a quasi-action by G on a tree whose space of ends contains the space of ends of G relative to f. This construction gives rise to examples of "exotic" quasi-actions on trees.

Keywords. Pseudocharacter, quasi-action, tree, bounded cohomology

AMS subject classification. Primary: 57M07. Secondary: 05C05, 20J06.

E-print: arXiv:math.GR/0303380

DOI: 10.2140/gt.2005.9.1147

Submitted to GT on 22 August 2003. (Revised 9 March 2005.) Paper accepted 8 June 2005. Paper published 14 June 2005.

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Jason Fox Manning
Mathematics 253--37, California Institute of Technology
Pasadena, CA 91125, USA
Email: manning@caltech.edu

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